Question: Simplify the following expression: $ a = \dfrac{5z - 3}{-6} - \dfrac{-9}{4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{5z - 3}{-6} \times \dfrac{4}{4} = \dfrac{20z - 12}{-24} $ Multiply the second expression by $\dfrac{-6}{-6}$ $ \dfrac{-9}{4} \times \dfrac{-6}{-6} = \dfrac{54}{-24} $ Therefore $ a = \dfrac{20z - 12}{-24} - \dfrac{54}{-24} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{20z - 12 - 54 }{-24} $ Distribute the negative sign: $a = \dfrac{20z - 12 - 54}{-24}$ $a = \dfrac{20z - 66}{-24}$ Simplify the expression by dividing the numerator and denominator by -2: $a = \dfrac{-10z + 33}{12}$